A Senegalese man has been arrested by Italian police over the murder of a US woman who was found in her Florence apartment.

The man, identified as Diaw Cheik Tidiane, met Ashley Olsen in a local nightclub and the two had consensual sex in her home while under the influence of alcohol and possibly drugs, according to prosecutors.

The 35-year-old American was strangled in the early hours of Friday last week, Florence's chief prosecutor Giuseppe Creazzo told a news conference.